text: The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects.  The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.  From the Womersley number it can be shown that the transient inertia force is represented by , and from the last term in the non-modified Navier-Stokes equation that viscous force is represented by  (subscript one indicates that the boundary layer thickness is that of the transient boundary layer). Setting the two forces equal to each other yields:
  Solving for  yields:
  Adding a characteristic length (L) to both sides gives the ratio:
  Therefore, it can be seen that when the flow has a high Womersley Number the transient boundary layer thickness is very small, when compared to the characteristic length, which for circular vessels is the radius.  As shown earlier the convective inertial force is represented by the term   ; equating that to the viscous force term yields:
  Solving for the convective boundary layer thickness yields:
  Factoring in a characteristic length gives the ratio:
  From the equation it is shown that for a flow with a large Reynolds Number there will be a correspondingly small convective boundary layer compared to the vessel’s characteristic length.  By knowing the Reynolds and Womersley numbers for a given flow it is possible to calculate both the transient and the convective boundary layer thicknesses, and relate them to a flow in another system. The boundary layer thickness is also useful in knowing when the fluid can be treated as an ideal fluid. This is at a distance that is larger than both boundary layer thicknesses.